Lesson_9 - 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 9 lebxz...

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Unformatted text preview: 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 9 lebxz `xity qixi` :dkixr oxia xnr ,cwy inrp x"c ,ipinipa a`ei 'text :ddbd uixw di`n :dqtcd xeliih gezit :dxcbd aiaq f ( x ) ly n xcqn xeliih mepilet f` x-a (zegtl) minrt n dxifb f ( x ) m` :`ed x T n ( x ) = f ( x ) + f ( x )( x- x ) + f 00 ( x ) 2! ( x- x ) 2 + ... + f ( n ) ( x ) n ! ( x- x ) n :zxvewn daizka ,e` T n ( x ) = n X k =0 f ( k ) ( x ) k ! ( x- x ) k . f ( x ) ly n xcqn oxelwn mepilet mb `xwp xeliih mepilet x = 0 xy`k :zexrd milawn n xcq cr eizexfbpe `edy n-l deey e` dphw dlrnn cigid mepiletd `ed T n ( x ) .1 :xnelk ,i- n-d xcqd cr dizexfbpe f milawny mikxrd mze` z` x dcewpa , ≤ k ≤ n ,T ( k ) n ( x ) = f ( k ) ( x ) yeniya oeirxd . f ( x ) ly sxbl aexw T n ( x ) ly sxbd x ly daiaqae T n ( x ) = f ( x ) .2 .lcbi n-y lkk xtzyi aexiwdy mieewn ep`y `ed xeliih mepileta 1 :`nbec : f ( x ) = ln(1- x ) ly n xcqn oxelwn mepilet aeyig (`) f ( x ) = ln(1- x ) f (0) = 0 f ( x ) =- 1 1- x f (0) =- 1 f 00 ( x ) =- 1 (1- x ) 2 f 00 (0) =- 1 f (3) ( x ) =- 2(1- x )- 3 f (3) (0) =- 2 f (4) ( x ) =- 2 · 3(1- x )- 4 f (4) (0) =- 2 · 3 =- 3! . . . . . . f ( k ) ( x ) =- ( k- 1) !(1- x )- k f ( k ) (0) =- ( k- 1) ! T n ( x ) = n X k =0 f ( k ) (0) x k k ! = n X k =1- ( k- 1)! x k k ! =- n X k =1 x k k :`ed g ( x ) = 1 1- x ly n xcqn oxelwn mepilet (a) T n ( x ) = n X k =0 x k = 1 + x + x 2 + ... + x n .` sirqa aeyigd lr jnzqpe g ( k ) ( x ) =- ( ln(1- x ) ) (...
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Lesson_9 - 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 9 lebxz...

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